tp0 . 0 0 . 4 0 . 8

Proof: Consideration of the way that the classifier scores are arranged shows that both x(t) and y(t) increase and decrease together as t varies. Moreover, limt→∞ x(t) = limt→∞ y(t) = 0 and limt→−∞ x(t) = limt→−∞ y(t) = 1, which establishes the result.